Lesson 17 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17
Objective: Use basic facts to estimate quotients with two-digit divisors.
Suggested Lesson Structure
Fluency Practice

Application Problem

Concept Development

Student Debrief

Total Time
(12 minutes)
(5 minutes)
(33 minutes)
(10 minutes)
(60 minutes)
Fluency Practice (12 minutes)
 Group Count by Multiples of 10 5.NBT.2
(5 minutes)
 Round to the Nearest Ten 5.NBT.4
(2 minutes)
 Divide by Multiples of 10, 100, and 1,000 5.NBT.6
(5 minutes)
Group Count by Multiples of 10 (5 minutes)
Note: Counting by multiples of 10 helps students estimate quotients with two-digit divisors during the
Concept Development.
Repeat the process in G5–M2–Lesson 16 for 4 tens, 5 tens, and 7 tens.
Round to the Nearest Ten (2 minutes)
Note: Rounding to whole numbers and one decimal place prepares students to estimate quotients.
Repeat the process in G5–M2–Lesson 16 for the following possible sequence: 21, 37, 16, 54, 73, 65, 25.
Divide by Multiples of 10, 100, and 1,000 (5 minutes)
Materials: (S) Personal white boards
Note: This drill reviews content from G5–M2–Lesson 16.
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(Write 700 ÷ 10.) Say the division sentence.
700 ÷ 10 = 70.
(Write 800 ÷ 20.) Write 800 ÷ 20 as a two-step division sentence taking out the ten.
(Write = 800 ÷ 10 ÷ 2.)
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
2.E.16
Lesson 17 5
NYS COMMON CORE MATHEMATICS CURRICULUM
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Below the two-step division sentence, rewrite it in one step after solving the first division problem.
(Write = 80 ÷ 2.)
Write the answer below 80 ÷ 2.
(Write = 40.)
Repeat the process for the following possible sequence: 15,000 ÷ 30, 15,000 ÷ 300, 15,000 ÷ 3,000, 450,000 ÷
50, and 21,000 ÷ 300.
Application Problem (5 minutes)
852 pounds of grapes were packed equally into 3 boxes for shipping.
How many pounds of grapes will there be in 2 boxes?
Note: The focus of this Application Problem is division with a onedigit divisor. This review encompasses both the meaning of and skill
with division, which helps students as they learn to work with a twodigit divisor.
Concept Development (33 minutes)
Materials: (S) Personal white boards
Note: The word whole is used throughout the module to indicate the
dividend. The choice of this term is two-fold. First, whole provides a
natural scaffold for the fraction work that is to come in Modules 3 and
4. Second, the words dividend and divisor are easily confused. While
the word dividend can certainly be included as well, students may find
whole to be a more meaningful term.
Problem 1: 402 ÷ 19
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(Write 402 ÷ 19 on the board.) What’s the whole in
this problem?
402.
What’s the divisor?
19.
Let’s round the divisor first. What is 19 rounded to the
nearest ten?
20.
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
NOTES ON
MULTIPLE MEANS OF
ENGAGEMENT:
Allow students to continue to use place
value disks or mats to represent the
division by multiples of 10 if this
scaffold is necessary.
Additionally, students may need to
continue to record the division
sentences in two steps similar to the
fluency activity above. For example,
Problem 1’s estimate could be written
as 400 ÷ 20 = 400 ÷ 10 ÷ 2 = 40 ÷ 2 = 20.
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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2.E.17
Lesson 17 5
NYS COMMON CORE MATHEMATICS CURRICULUM
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Let’s record our estimation. (Under the original
problem, write ൎ ____ ÷ 20 on the board.) We need to
round our whole, 402, to a number that can easily be
divided by 20. Turn and share your ideas with your
partner. (Allow time for students to share.)
What should we round 402 to?
I can round 402 to 400.  I can use mental math to
divide 400 by 20.
(Fill in the blank to get ൎ 400 ÷ 20.) What is 400
divided by 20? Turn and share.
400 divided by 10 is 40. 40 divided by 2 is 20.  400
divided by 2 equals 200. 200 divided by 10 equals 20.
Yes. We know that 400 divided by 20 is equal to 40
divided by 2. (Write 40 ÷ 2 below 400 ÷ 20.) What is
our estimated quotient?
20.
NOTES ON
MULTIPLE MEANS
OF ACTION AND
EXPRESSION:
Problem 2: 149 ÷ 71
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(Write 149 ÷ 71 on the board.) Take out your personal
board. To estimate the quotient, what do we do first?
Having students write the multiples in a
Round the divisor.
vertical or horizontal list as they count
Do it now.
can provide a helpful support.
(Round to 70.)
(Write ≈____ ÷ 70 on the board.) Now round the
whole, 149. Usually when we round, we round to
place value units. But since we’re dividing, it’d be
really nice if our whole was a multiple of the divisor.
So let’s round it to the nearest multiple of 70. Count
with me by seventies.
70, 140, 210, 280.
Our whole is between which of these?
140 and 210.
We are rounding to the nearest multiple of 70. 149 is
closest to which multiple of 70?
140.
(Fill in ≈ 140 ÷ 70.) 140 divided by 70 is the same as 14 divided by what? Say the division sentence.
14 ÷ 7 = 2.
How do you know?
140 ÷ 70 = 140 ÷ 10 ÷ 7.  Dividing by 70 is the same as dividing by 10 and then dividing by 7.  If I
put parentheses like this (140 ÷ 10) ÷ 7, it’s easy to see the two expressions are equal.
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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2.E.18
Lesson 17 5
NYS COMMON CORE MATHEMATICS CURRICULUM
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So, what’s 140 ÷ 70 then?
2.
(Record =14 ÷ 7 = 2.) Good. Our estimated quotient is 2.
Problem 3: 427 ÷ 58
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(Write 427 ÷ 58 on the board.) Work with a partner and solve
this problem.
What’s the estimated divisor?
60.
So 60 will be our unit. Let’s count by sixties and stop when we
find a multiple near 427.
60, 120, 180, 240, 300, 360, 420… stop!
To what number should we round the whole?
420.
What’s the next multiple of 20?
440.
Is 427 closer to 420 or 440?
420.
Then let's use 420 as our estimated whole. 420 divided by 60 is the same as what division equation?
42 ÷ 6 = 7.
Share with your partner how you know.
420 ÷ 60 = 420 ÷ 10 ÷ 6.  It’s 42 tens divided by 6 tens. It’s like 10 divided by 10 is 1, so you are
just left with 42 divided by 6.  If I write 42 x 10 ÷ 10 ÷ 6, it’s easy to see that multiplying by 10 and
dividing by 10 equals 1 so we are left with 42 divided by 6.  420 ÷ 60 = 42 ÷ 6.
What is our estimated quotient? What’s 420 divided by 60?
7.
Yes. The estimated quotient is 7.
Problem 4: 293 ÷ 42
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(Write 293 ÷ 42 on the board.) Round the divisor.
40.
(Write ≈____ ÷ 40 on the board.) So, 40 is our unit.
Round the whole to a multiple of 40. Whisper the
multiples of 40 to your neighbor. Stop when you hear
a multiple that is near our whole.
40, 80, 120, 160, 200, 240, 280, 320.
I see you went past 293 this time. Our total is between which two multiples of 40?
280 and 320.
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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2.E.19
Lesson 17 5
NYS COMMON CORE MATHEMATICS CURRICULUM
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Visualize a number line. Which multiple is closer to 293?
280.
Finish the division problem on your personal board. Compare your work with a neighbor.
Tell me how to estimate the quotient.
280 ÷ 40 = 28 ÷ 4 = 7.
Problem 5: 751 ÷ 93
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(Write 751 ÷ 95 on the board.) Work independently to solve
this problem.
Share your work with a neighbor.
What was your estimated divisor?
90.
And the estimated whole?
720.
Tell me how to estimate the quotient.
720 ÷ 90 = 72 ÷ 9 = 8.
Problem Set (10 minutes)
Students should do their personal best to complete the
Problem Set within the allotted 10 minutes. For some
classes, it may be appropriate to modify the assignment
by specifying which problems they work on first. Some
problems do not specify a method for solving. Students
solve these problems using the RDW approach used for
Application Problems.
Student Debrief (10 minutes)
Lesson Objective: Use basic facts to estimate quotients
with two-digit divisors.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers
with a partner before going over answers as a class.
Look for misconceptions or misunderstandings that can
be addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process
the lesson. You may choose to use any combination of
the questions below to lead the discussion.
Lesson 17:
Date:
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Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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2.E.20
Lesson 17 5
NYS COMMON CORE MATHEMATICS CURRICULUM




Look back at the divisors in Problem 1 (l), (m),
and (n). What did you notice about them?
How did the 5 in the ones place affect the way
you rounded?
In Problem 1(o), did anyone leave the divisor
11, unrounded? Is it always necessary to
round? (Some students may have estimated
660 ൊ 10 and others may have seen 660 ൊ 11.)
Do we follow our typical rounding rules when
estimating with division? Why not? We don’t
always follow our typical rules of rounding to
certain place value units because we are
looking for easy multiples of our unit (divisor).
Sometimes that means we choose a number
that is farther away from our actual whole
than rounding by place value would produce.
Problem 3 provides an opportunity for
students to discuss division by multiples of 10.
Students might justify their answers using
place value disks or two-step division
sentences.
Exit Ticket (3 minutes)
After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you
assess the students’ understanding of the concepts that were presented in the lesson today and plan more
effectively for future lessons. You may read the questions aloud to the students.
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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2.E.21
Lesson 17 Problem Set 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Date
1. Estimate the quotient for the following problems. Round the divisor first.
d.
≈ 600 ÷ 20
≈ _________ ÷ _________
≈ _________ ÷ _________
= 30
= _________
= _________
e.
141 ÷ 73
f.
241 ÷ 58
482 ÷ 62
≈ _________ ÷ _________
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
= _________
h.
g. 656 ÷ 81
j.
c. 826 ÷ 37
b. 913 ÷ 29
a. 609 ÷ 21
i.
799 ÷ 99
635 ÷ 95
≈ _________ ÷ _________
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
= _________
l.
k. 648 ÷ 83
311 ÷ 76
143 ÷ 35
≈ _________ ÷ _________
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
= _________
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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2.E.22
Lesson 17 Problem Set 5
NYS COMMON CORE MATHEMATICS CURRICULUM
o. 667 ÷ 11
n. 552 ÷ 85
m. 525 ÷ 25
≈ _________ ÷ _________
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
= _________
2. A video game store has a budget of $825 and would like to purchase new video games. If each video
game costs $41, estimate the total number of video games the store can purchase with their budget.
Explain your thinking.
3. Jackson estimated 637 ÷ 78 as 640 ÷ 80. He reasoned that 64 tens divided by 8 tens should be 8 tens. Is
Jackson’s reasoning correct? If so, explain why. If not, explain a correct solution.
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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2.E.23
Lesson 17 Exit Ticket 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Date
1. Estimate the quotient for the following problems.
b. 913 ÷ 31
a. 608 ÷ 23
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
d. 481 ÷ 68
c. 151 ÷ 39
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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2.E.24
Lesson 17 Homework 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Date
1. Estimate the quotient for the following problems. The first one is done for you.
a. 821 ÷ 41
b. 617 ÷ 23
≈ 800 ÷ 40
≈ _________ ÷ _________
≈ _________ ÷ _________
= 20
= _________
= _________
d. 482 ÷ 52
e. 531 ÷ 48
f. 141 ÷ 73
≈ _________ ÷ _________
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
= _________
g. 476 ÷ 81
j.
c. 821 ÷ 39
h. 645 ÷ 69
i.
599 ÷ 99
≈ _________ ÷ _________
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
= _________
k. 729 ÷ 81
301 ÷ 26
≈ _________ ÷ _________
= _________
≈ _________ ÷ _________
= _________
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
l.
636 ÷ 25
≈ _________ ÷ _________
= _________
Use basic facts to approximate quotients with two-digit divisors.
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2.E.25
Lesson 17 Homework 5
NYS COMMON CORE MATHEMATICS CURRICULUM
m. 835 ÷ 89
n. 345 ÷ 72
o. 559 ÷ 11
≈ _________ ÷ _________
≈ _________ ÷ _________
≈ _________ ÷ _________
= _________
= _________
= _________
2. Mrs. Johnson spent $611 buying lunch for 78 students. If all of the lunches were the same cost, about
how much did she spend on each lunch?
3. An oil well produces 172 gallons of oil every day. A standard oil barrel holds 42 gallons of oil. About how
many barrels of oil will the well produce in one day? Explain your thinking.
Lesson 17:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Use basic facts to approximate quotients with two-digit divisors.
4/2/14
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
2.E.26